On stochastic modelling of linear circuits

In this paper, ant colony optimization (ACO) algorithm is presented, as a tool to find transistor sizes in digital circuits. Performance of ACO has been tested on four digital circuits, of different complexity, to find optimum balance between power and delay of circuits. Optimization problem has been set up by first, formulating an objective function, to be minimized, for each circuit and then finding the values of variables of circuits, using optimization algorithm. For the purpose of examining the results, circuits are optimized using genetic algorithm (GA) also. Results show that, ACO performs better than GA, for all the four circuits, in finding optimized transistor sizes.

Section: Three Input Nand Gatementioning

confidence: 99%

“…Results from the optimized flip-flop show large reduction in power delay product (PDP), as compared to, flip-flop with transistor sizes, without optimization. In [8] also, linear circuits are modeled using stochastic modeling.…”

mentioning

confidence: 99%

Transistor size optimization in digital circuits using ant colony optimization for continuous domain

Gupta

Ghosh

2012

“…This is because, for numerical efficiency reasons, simulation tools are mainly developed in the frequency domain whereas phase-noise effect is a typical time-domain phenomenon: it arises from the stochastic diffusion process or random walk that the oscillator's phase undergoes in time due to small-amplitude noisy perturbations [5,11]. Time-domain analysis [19] of the phase-diffusion process is thus the prime way to achieve realistic predictions of phase-noise and to deduce design guidelines.…”

Section: Introductionmentioning

confidence: 99%

Time‐domain analysis of phase‐noise and jitter in oscillators due to white and colored noise sources

Maffezzoni

D'Amore

2011

SUMMARYThis paper presents an original time-domain analysis of the phase-diffusion process, which occurs in oscillators due to the presence of white and colored noise sources. It is shown that the method supplies realistic quantitative predictions of phase-noise and jitter and provides useful design-oriented closed-form expressions of such phenomena. Analytical expressions and numerical simulations are verified through measurements performed on a relaxation oscillator whose behavior is perturbed by externally controlled noise sources.

“…Thermal effects on the reliability and performance of VLSI design have attracted increasing attention due to the rapid increase of power and package densities in recent years. Thermal effects are of great importance to a variety of problems including circuit design [1,2], thermodynamical analysis [3], electrothermal stability [4] and thermal noise analysis [5,6], etc. More and more efforts have been put into the development of numerical methods for the solution of heat conduction problems.…”

Section: Introductionmentioning

confidence: 99%

“…(4) Although block cyclic reduction and D i , S i method are computationally more expensive than direct computation, divide-and-conquer algorithm emerges for the very first time in the literature to solve large-scale block-tridiagonal systems. (5) Thermal ADI is applied to the proposed schemes in 2-D and 3-D cases.…”

Section: Introductionmentioning

confidence: 99%

Finite difference schemes for heat conduction analysis in integrated circuit design and manufacturing

Shen¹,

Wong²,

Lam³

et al. 2011

SUMMARYThe importance of thermal effects on the reliability and performance of VLSI circuits has grown in recent years. The heat conduction problem is commonly described as a second-order partial differential equation (PDE), and several numerical methods, including simple explicit, simple implicit and Crank-Nicolson methods, all having at most second-order spatial accuracy, have been applied to solve the problem. This paper reviews these methods and further proposes a fourth-order spatial-accurate finite difference scheme to better approximate the PDE solution. Moreover, we devise a fourth-order accurate approximation of the convection boundary condition, and apply it to the proposed finite difference scheme. We use a block cyclic reduction and a recently developed numerically stable algorithm for inversion of block-tridiagonal and banded matrices to solve the PDE-based system efficiently. Despite their higher computation complexity than direct computation in a sequential processor, we make it possible for the very first time to employ a divide-and-conquer algorithm, viable for parallel computation, in heat conduction analysis. Experimental results prove such possibility, suggesting that applying divide-and-conquer algorithms, higher-order finite difference schemes can achieve better simulation accuracy with even faster speed and less memory requirement than conventional methods.